Why more matters appear in hot equator, when they should flow to the cold poles?

Question

I am reading a paper* about the application of the maximum entropy production (MEP) in Earth science (I'm new to MEP btw). The authors start with the system of gas molecules first. When the system is isolated, it has the maximum entropy and the molecules are distributed randomly. When it get contacted with the hot reservoir, nearby molecules will have higher energy, therefore moving faster and will tend to move to the other side, while colder molecules are not really active, so they will stay in their positions. As a consequence. the molecules will shift to the cold side.

When we replace the hot reservoir with the equator, and the cold reservoir with the pole, we will have the model of planetary system.

However, doesn't that mean that more matter will locate in the pole(s) than the equator? In Earth, this would mean that there will be more structured or ordered matters, including organisms in the poles than the equator. This doesn't look right to what we know.

How can this be explained?

_{*The Maximum Entropy Production Principle: Its Theoretical Foundations and Applications to the Earth System}

Answer 1

This is very simple to explain when we consider that the 'model' you have been presented with is a gross oversimplification - a one dimensional mechanism. But the Earth is a multi-phase (air water ice), three dimensional system in which convective currents circulate. Hence there is a counterflow of both air and ocean currents in addition to the basic entropy model. The entire thermal circulation is also massively influenced by considerations of conservation of mass, conservation of energy, and conservation of angular momentum. Its a pretty complex system, as climate modellers are only too aware, and cannot be reduced to any simple model.